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Recall that the electrostatic potential energy of interaction between two charges \(q_1\) and \(q_2\) that are separated by a distance \(r_{12}\) is \((1/4\pi \epsilon_0)q_1q_2/r_{12}\). Here, \(q_1 = +e\) is the charge of the nucleus in the hydrogen atom (the charge of the proton), \(q_2 = -e\) is the charge of the electron and \(r_{12} = r_n ...
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Technical note: an allowed orbit is one in which the electron mass times its speed times the radius of the orbit is equal to a positive integer n times Planck's constant divided by 2 pi. The integer n can be 1, 2, 3, 17, 108, etc.
19 sie 2024 · In the quantum-mechanical model of an atom, which is the modern and currently accepted model, the location of electrons in the atom are described by four quantum numbers, not just the one predicted by Bohr.
30 cze 2023 · \[E_{total}=\underset{\text{kinetic energy}}{\dfrac{p^2}{2m_e}} - \underset{\text{potential energy}}{\dfrac{Ze^2}{4\pi \epsilon_0 r}} \label{1.8.8}\] The force on the electron is \[\vec{F}=-\dfrac{Ze^2}{4\pi \epsilon_0 r^3}r \label{1.8.9}\] and its magnitude is
23 lip 2021 · The full Hamiltonian operator for each electron consists of the kinetic energy term \(\dfrac {-\hbar ^2}{2m} \dfrac {d^2}{dx^2}\) and the sum of the Coulomb potential energy terms \(\dfrac {q_1q_2}{4\pi \epsilon _0 r_{12}}\) for the interaction of each electron with all the other electrons and with the nuclei (\(q\) is the charge on each ...
\[v = \frac{MZe^2}{4 \pi \epsilon_0 ( M +m) \hbar n}. \label{7.4.5}\] The energy of the atom is the sum of the mutual potential energy between nucleus and electron and the orbital kinetic energies of the two particles. That is: \[ E = -\frac{Ze^2}{4 \pi \epsilon_0 a} + \frac{1}{2} m v^2 + \frac{1}{2} M \left( \frac{mv}{M} \right)^2 . \label{7.4 ...
